On the complementary nabla Pachpatte type dynamic inequalities via convexity

Pachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining these concepts will lead to more significant applications that can be used to...

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Main Authors: Zeynep Kayar, Billur Kaymakcalan
Format: Article
Language:English
Published: Elsevier 2024-01-01
Series:Kuwait Journal of Science
Subjects:
Online Access:https://www.sciencedirect.com/science/article/pii/S2307410823001554
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author Zeynep Kayar
Billur Kaymakcalan
author_facet Zeynep Kayar
Billur Kaymakcalan
author_sort Zeynep Kayar
collection DOAJ
description Pachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining these concepts will lead to more significant applications that can be used to develop certain branches of mathematics such as fuctional analysis, operator theory, optimization and ordinary/partial differential equations. We extend classical nabla Pachpatte type dynamic inequalities by changing the interval of the exponent δ from δ ​> ​1 to δ ​< ​0. Our results not only complement the classical nabla Pachpatte type inequalities but also generalize complementary nabla Hardy-Copson type inequalities. As the case of δ ​< ​0 has not been previously examined, these complementary inequalities represent a novelty in the nabla time scale calculus, specialized cases in continuous and discrete scenarios, and in the dual outcomes derived in the delta time scale calculus.
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spelling doaj-art-bd9cda35493e40a7b3fd0437d73bc9ab2025-08-20T03:19:57ZengElsevierKuwait Journal of Science2307-41162024-01-01511100130https://doi.org/10.1016/j.kjs.2023.09.004On the complementary nabla Pachpatte type dynamic inequalities via convexityZeynep Kayar0https://orcid.org/0000-0002-8309-7930Billur Kaymakcalan1https://orcid.org/0000-0002-0763-9128Dept. of Mathematics, Van Yuzuncu Yil University, 65080, Van, TurkeyDept. of Mathematics, Çankaya University, 06810, Ankara, TurkeyPachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining these concepts will lead to more significant applications that can be used to develop certain branches of mathematics such as fuctional analysis, operator theory, optimization and ordinary/partial differential equations. We extend classical nabla Pachpatte type dynamic inequalities by changing the interval of the exponent δ from δ ​> ​1 to δ ​< ​0. Our results not only complement the classical nabla Pachpatte type inequalities but also generalize complementary nabla Hardy-Copson type inequalities. As the case of δ ​< ​0 has not been previously examined, these complementary inequalities represent a novelty in the nabla time scale calculus, specialized cases in continuous and discrete scenarios, and in the dual outcomes derived in the delta time scale calculus.https://www.sciencedirect.com/science/article/pii/S2307410823001554time scale calculushardy's inequalitycopson's inequalitypachpatte's inequalityconvexity
spellingShingle Zeynep Kayar
Billur Kaymakcalan
On the complementary nabla Pachpatte type dynamic inequalities via convexity
Kuwait Journal of Science
time scale calculus
hardy's inequality
copson's inequality
pachpatte's inequality
convexity
title On the complementary nabla Pachpatte type dynamic inequalities via convexity
title_full On the complementary nabla Pachpatte type dynamic inequalities via convexity
title_fullStr On the complementary nabla Pachpatte type dynamic inequalities via convexity
title_full_unstemmed On the complementary nabla Pachpatte type dynamic inequalities via convexity
title_short On the complementary nabla Pachpatte type dynamic inequalities via convexity
title_sort on the complementary nabla pachpatte type dynamic inequalities via convexity
topic time scale calculus
hardy's inequality
copson's inequality
pachpatte's inequality
convexity
url https://www.sciencedirect.com/science/article/pii/S2307410823001554
work_keys_str_mv AT zeynepkayar onthecomplementarynablapachpattetypedynamicinequalitiesviaconvexity
AT billurkaymakcalan onthecomplementarynablapachpattetypedynamicinequalitiesviaconvexity